# If all the premises of an argument are true, is the argument logically valid?

Where an argument is said to be logically valid "if and only if it is not possible for the premises to e true and the conclusion false".

I know that the argument is indeed logically valid if all the premises are logically true, through I am confused if the same reasoning applies to 'true' premises, because it is possible for all the premises to be true but for the conclusion to not follow from them--in such a case, is the argument valid?

• possible duplicate of logical form of the definition of validity Commented Jan 11, 2015 at 23:55
• Well... since 1+1=2, and also red mixed with yellow produces orange, there must be a universal "Designer". My premises are all true, my conclusion I think is worth questioning, rather than not. True premises are not a promise of a valid conclusion. I do agree. Commented Feb 8 at 9:01

It is easy to come up with a set of premises that are all true, or logically true, but have the conclusion drawn from them be invalid. The most obvious way would be by not having a full enough set of premises. It would not be fair to say...

All humans are primates. All primates are mammals. Therefore all mammals are orange.

The conclusion is not explicitly derived from the premises, but can still be presented in this way.

It's trivially easy to come up with an invalid argument with either conditionally true or logically true premises --just attach it to a false conclusion.

On the other hand, every argument that ends with a logically true conclusion is valid, regardless of the premises.

If you carefully reread the definition you provided, you will see how both the statements above follow from it.

Consider the argument with no premises and the conclusion "the sky is red". All the premises are (vacuously) true --- and surely "logically true", whatever you might mean by that --- but surely the conclusion is false and the argument is not valid.

This is no better than R. Barzell's example, but it's even simpler. And it addresses your distinction between "true" and "logically true", by providing a list of premises all of which are true, all of which are logically true (again, whatever that means), all of which are false, all of which are logically false, and all of which have property glarb, whatever that might be.

• Although nobody thinks that there can be arguments without premises. And if there are no premises, why on earth would the premises be true? That sound weird. Commented Jan 10, 2015 at 10:39
• Of course there are arguments without premises. A valid argument consists of a set of premises and a list of statement, each of which is either a premise or a valid inference from earlier statements. Nothing in that definition says that the set of premises has to be non-empty. There is thus exactly one valid argument (along with a great number of invalid arguments) with no premises. Commented Jan 10, 2015 at 14:29
• @Lukas: If nevertheless you inisist on a specific source, try the first sentence of the Wikipedia page on formal proof: en.wikipedia.org/wiki/Formal_proof . Commented Jan 10, 2015 at 17:29
• @Lukas: It also doesn't say there that the number of premises can be exactly two. Do you conclude that the number of premises can't be exactly two? Commented Jan 10, 2015 at 19:58
• @Lukas: You are just making this up. You can make up any rules you want, but that doesn't mean the rest of the world has to follow them. An argument starts with a set of premises. It is nowhere explicitly stated that the number of premises can be even; nevertheless, the number of premises can be even. It is nowhere explicitly stated that the number of premises can be prime; nevertheless, the number of premises can be prime. It is nowhere explicitly stated that the number of premises can be zero; nevertheless, the number of premises can be zero. (CTD) Commented Jan 11, 2015 at 0:04